The "-nom-" of "ignominious" comes from "nomen," the Latin word for "name" or “repute.” (It's also the root of "misnomer," "nomenclature," and "nominal," among others.) The "ig-" part of the word is akin to the negative prefix "in-"; when joined to the root "-nom-," it indicates the namelessness that goes with shame or dishonor. To suffer an ignominious fate is to lose the opportunity to make a name for oneself or to lose one’s good name. When "ignominious" was first borrowed from a French form of the word in the 15th century, it meant "disgraced" or "dishonorable." "Ignominious" continues to have such meanings, but it also has somewhat milder meanings — "embarrassing" and "humiliating."